Scalars & Vectors (Cambridge International IGCSE Physics)

Scalar & vector quantities

Spec point — 1.1.2 · Understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction

Extended Tier Only

• All quantities can be one of two types:

  • A scalar
  • A vector

Scalars

• Scalar quantities have only a magnitude

  • Mass is an example of a scalar quantity because it has magnitude without direction
  • Energy and time are also examples of scalar quantities

Vectors

• Vector quantities have both magnitude and direction

  • Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction
  • Acceleration and momentum are also examples of vector quantities

Distance and displacement

• Distance is a measure of how far an object has travelled, regardless of direction

  • Distance is the total length of the path taken
  • Distance, therefore, has a magnitude but no direction
  • So, distance is a scalar quantity

• Displacement is the distance between two points in a straight line, in a stated direction

  • So, displacement is a vector quantity

Displacement is a vector quantity, while distance is a scalar quantity

Speed and velocity

• Speed is a measure of the distance travelled by an object per unit time, regardless of the direction

  • So, speed is a scalar quantity

• Velocity is the speed of an object in a given direction

  • So, velocity is a vector quantity

Exam Hint Make sure you are comfortable with the differences between similar scalars and vectors.

The most commonly confused pairings tend to be:

• speed and velocity
• mass and weight

Examples of scalars & vectors

Spec point — 1.1.2 · Know that the following quantities are scalars: distance, speed, time, mass, energy and temperature Know that the following quantities are vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength

Examples of scalars & vectors

Extended Tier Only

• The table below lists some common examples of scalar and vector quantities
• Corresponding scalars and their vector counterparts are aligned in the table where applicable

Worked Example State what is meant by a scalar quantity and give two examples.

[3]

Answer:

Step 1: Recall the definition of a scalar quantity

• Scalars are quantities that have only a magnitude [1 mark]

Step 2: Name two examples of scalar quantities

Any two from:

• Distance
• Speed
• Time
• Mass
• Energy
• Temperature

[2 marks]